**Rotation and Translation of Triangles**In the diagram shown, triangle $ \triangle JKL $ has been rotated 270° counterclockwise about point $ J $, resulting in triangle $ \triangle J'K'L' $. **Graph Explanation:**- The graph is a coordinate plane with the x-axis and y-axis ranging from -8 to 8.- The original triangle $ \triangle JKL $ has the following coordinates: $ J (1, 2) $, $ K (4, 1) $, and $ L (4, 4) $.- After the rotation, the new triangle $ \triangle J'K'L' $ is formed at the coordinates: $ J' (1, 2) $, $ K' (2, -1) $, and $ L' (-1, -1) $.- A second triangle $ \triangle RST $ is shown in red, with coordinates $ R (2, -3) $, $ S (5, -4) $, and $ T (5, -7) $.**Translation Task:**The task is to determine the rule that will translate triangle $ \triangle J'K'L' $ onto triangle $ \triangle RST $.**Graph Elements:**- Points are represented as filled circles.- Vectors connect the vertices of each triangle.- $\triangle JKL$ and $\triangle J'K'L'$ are in black, while $\triangle RST$ is in red.**Interactive Components:**- There are dropdown menus below the graph to select transformation rules for both x and y coordinates.**Problem-Solving Strategy:**To find the translation rule, observe the horizontal and vertical shifts needed to align corresponding points of $ J' $ with $ R $, $ K' $ with $ S $, and $ L' $ with $ T $. Analyze changes in x and y coordinates accordingly.

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Description: **Rotation and Translation of Triangles**In the diagram shown, triangle $ \triangle JKL $ has been rotated 270° counterclockwise about point $ J $, resulting in triangle $ \triangle J'K'L' $. **Graph Explanation:**- The graph is a coordinate p

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Below A JKL was rotated 270 counterclockwise about point J to create AJ'K'L What would be rule that would translate A JKL onto A RST?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

**Rotation and Translation of Triangles**

In the diagram shown, triangle $ \triangle JKL $ has been rotated 270° counterclockwise about point $ J $, resulting in triangle $ \triangle J'K'L' $.

**Graph Explanation:**
- The graph is a coordinate plane with the x-axis and y-axis ranging from -8 to 8.
- The original triangle $ \triangle JKL $ has the following coordinates: $ J (1, 2) $, $ K (4, 1) $, and $ L (4, 4) $.
- After the rotation, the new triangle $ \triangle J'K'L' $ is formed at the coordinates: $ J' (1, 2) $, $ K' (2, -1) $, and $ L' (-1, -1) $.
- A second triangle $ \triangle RST $ is shown in red, with coordinates $ R (2, -3) $, $ S (5, -4) $, and $ T (5, -7) $.

**Translation Task:**
The task is to determine the rule that will translate triangle $ \triangle J'K'L' $ onto triangle $ \triangle RST $.

**Graph Elements:**
- Points are represented as filled circles.
- Vectors connect the vertices of each triangle.
- $\triangle JKL$ and $\triangle J'K'L'$ are in black, while $\triangle RST$ is in red.

**Interactive Components:**
- There are dropdown menus below the graph to select transformation rules for both x and y coordinates.

**Problem-Solving Strategy:**
To find the translation rule, observe the horizontal and vertical shifts needed to align corresponding points of $ J' $ with $ R $, $ K' $ with $ S $, and $ L' $ with $ T $. Analyze changes in x and y coordinates accordingly.

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